Inversion Symmetry of Gravitational Coupling in Cubic String Field Theory

TL;DR

This paper explores the inversion symmetry of gravitational coupling in cubic string field theory, revealing a new term that reconciles differences between canonical energy and gauge invariant observable.

Contribution

It introduces a new term in the gravitational coupling that restores inversion symmetry and aligns the gauge invariant observable with canonical energy.

Findings

Canonical energy exhibits inversion symmetry under K=0 and K=∞ exchange.

A new term in gravitational coupling accounts for the energy discrepancy.

The combined energy expression maintains inversion symmetry.

Abstract

It was found that the canonical energy of multi-brane solutions in CSFT constructed by the KBc algebra has a symmetry under the exchange of K=0 and K=\infty (inversion symmetry). On the other hand, the gauge invariant observable (GIO), which is regarded as the energy defined by the gravitational coupling of open string, cannot count the energy from K=\infty and therefore is not equal to the canonical energy. To resolve this discrepancy, we examine the recent argument of Baba and Ishibashi which directly relates the two energies. We find that the gravitational coupling which is equivalent to the canonical energy consists of the GIO and another new term, and the whole has the inversion symmetry.